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Dineutron correlations and BCS-BEC crossover in nuclear matter with the Gogny pairing force

The dineutron correlations and the crossover from superfluidity of neutron Cooper pairs in the $^1S_0$ pairing channel to Bose-Einstein condensation (BEC) of dineutron pairs in both symmetric and neutron matter are studied within the relativistic Hartree-Bogoliubov theory, with the effective interaction PK1 of the relativistic mean-field approach in the particle-hole channel and the finite-range Gogny force in the particle-particle channel. The influence of the pairing strength on the behaviors of dineutron correlations is investigated. It is found that the neutron pairing gaps at the Fermi surface from three adopted Gogny interactions are smaller at low densities than the one from the bare nucleon-nucleon interaction Bonn-B potential. From the normal (anomalous) density distribution functions and the density correlation function, it is confirmed that a true dineutron BEC state does not appear in nuclear matter. In the cases of the Gogny interactions, the most BEC-like state may appear when the neutron Fermi momentum $k_{Fn}\thicksim0.3 \rm{fm^{-1}}$. Moreover, based on the newly developed criterion for several characteristic quantities within the relativistic framework, the BCS-BEC crossover is supposed to realize in a revised density region with $k_{Fn}\in[0.15,0.63] \rm{fm^{-1}}$ in nuclear matter.